If \(\overset{\circ }{S} \)  is not empty, then \(S\)  cannot have isolated edges and \(S\)  has a positive reach in the sense of Federer [1]} because the curvature on the compact edges is bounded. Therefore,
\(\sigma _2(S^{+\epsilon })=\chi (S)\pi \epsilon ^2+\textnormal {OMC}(S)\epsilon +\sigma _2(S),\) 
